Properties

Label 1210.2.l
Level $1210$
Weight $2$
Character orbit 1210.l
Rep. character $\chi_{1210}(233,\cdot)$
Character field $\Q(\zeta_{20})$
Dimension $432$
Sturm bound $396$

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Defining parameters

Level: \( N \) \(=\) \( 1210 = 2 \cdot 5 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1210.l (of order \(20\) and degree \(8\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 55 \)
Character field: \(\Q(\zeta_{20})\)
Sturm bound: \(396\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1210, [\chi])\).

Total New Old
Modular forms 1776 432 1344
Cusp forms 1392 432 960
Eisenstein series 384 0 384

Trace form

\( 432q + 8q^{3} + 8q^{5} + 20q^{7} + O(q^{10}) \) \( 432q + 8q^{3} + 8q^{5} + 20q^{7} + 32q^{12} + 20q^{15} + 108q^{16} + 20q^{17} + 8q^{20} + 24q^{23} + 8q^{25} - 8q^{26} - 16q^{27} + 20q^{28} - 16q^{31} + 124q^{36} - 32q^{37} + 36q^{38} + 20q^{41} + 20q^{42} - 64q^{45} - 40q^{46} - 36q^{47} - 8q^{48} - 40q^{50} - 40q^{51} - 40q^{52} - 4q^{53} + 8q^{56} - 48q^{58} - 16q^{60} - 80q^{61} - 40q^{62} - 100q^{63} + 16q^{67} - 20q^{68} + 72q^{70} + 96q^{71} + 20q^{73} + 88q^{75} - 16q^{78} + 12q^{80} + 228q^{81} + 16q^{82} + 80q^{85} + 56q^{86} + 80q^{90} + 68q^{91} + 16q^{92} - 76q^{93} - 20q^{95} - 84q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1210, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1210, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1210, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(55, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(110, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(605, [\chi])\)\(^{\oplus 2}\)